具有媒体报道的时滞SVIRS传染病模型的稳定性与Hopf分支
Stability and Hopf Bifurcation of a Delayed SVIRS Epidemic Model with Media Coverage
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中文总结 AI 辅助
本文构建纳入媒体报道等因素的时滞SVIRS传染病模型，分析其平衡点稳定性与Hopf分支，证实更强媒体干预可抑制疫情振荡，为传染病防控提供理论支撑。
中文摘要 AI 辅助
本文构建并分析了一个时滞SVIRS传染病模型，该模型纳入了媒体报道效应、疫苗接种、免疫力衰减、康复后暂时免疫力、饱和治疗以及媒体报道诱导的延迟行为反应。文中证明了解的正性与一致有界性，推导了基本再生数，并研究了无病平衡点和地方病平衡点的局部与全局渐近稳定性。以媒体诱导的行为延迟作为Hopf分支参数，得到了临界延迟阈值，当延迟超过该阈值时，地方病平衡点将失去稳定性并出现周期性振荡。运用中心流形和规范型理论确定了局部Hopf分支的方向以及分岔周期解的稳定性，同时采用全局Hopf分支定理建立了周期解分支的无界延拓。数值模拟验证了理论结果，表明更强的媒体干预可抑制疫情振荡并提升系统稳定性。这些发现揭示了多种流行病学机制与延迟媒体反应的耦合效应，为设计有效的传染病防控策略提供了理论支撑。
英文摘要
This paper formulates and analyzes a delayed SVIRS epidemic model incorporating media coverage effects, vaccination, waning immunity, temporary post-recovery immunity, saturated treatment, and delayed behavioral responses induced by media coverage. The positivity and uniform boundedness of solutions are established, the basic reproduction number is derived, and the local and global asymptotic stability of the disease-free and endemic equilibria is investigated. Taking the media-induced behavioral delay as the Hopf bifurcation parameter, a critical delay threshold is obtained, beyond which the endemic equilibrium loses stability and periodic oscillations emerge. Center manifold and normal form theories are applied to determine the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions, while a global Hopf bifurcation theorem is used to establish the unbounded continuation of the periodic solution branch. Numerical simulations confirm the theoretical results and indicate that stronger media intervention can suppress epidemic oscillations and enhance system stability. These findings reveal the coupled effects of multiple epidemiological mechanisms and delayed media responses, providing theoretical support for the design of effective infectious disease control strategies.
